Let ABC be a triangle formed by the lines 7 x -6 y +3=0, x +2 y -31=0 and 9 x -2 y -19=0. Let the point (h, k) be the image of the centroid of Δ ABC…

Let ABC be a triangle formed by the lines $\displaystyle 7 \mathrm{x}-6 \mathrm{y}+3=0, \mathrm{x}+2 \mathrm{y}-31=0$ and $\displaystyle 9 \mathrm{x}-2 \mathrm{y}-19=0$. Let the point (h, k) be the image of the centroid of $\displaystyle \Delta \mathrm{ABC}$ in the line 3x+6y -$\displaystyle 53$=0. Then $\displaystyle \mathrm{h}^2+\mathrm{k}^2+\mathrm{hk}$ is equal to :